TITLE: Philosophy behind Yitang Zhang's work on the Twin Primes Conjecture
QUESTION [100 upvotes]: Yitang Zhang recently published a new attack on the Twin Primes Conjecture. Quoting Andre Granville :

“The big experts in the field had
  already tried to make this approach
  work,” Granville said. “He’s not a
  known expert, but he succeeded where
  all the experts had failed.”

What new approach did Yitang Zhang try & what did the experts miss in the first place?

REPLY [3 votes]: At a fairly non-detailed level, the Simons Foundation has a nice article on the subject, which I understand has also been picked up by Wired:
https://www.simonsfoundation.org/features/science-news/unheralded-mathematician-bridges-the-prime-gap/
To summarize very briefly, he is building on work by Goldston, Pintz, and Yıldırım.  The article describes his innovation as "... to use not the GPY sieve but a modified version of it, in which the sieve filters not by every number, but only by numbers that have no large prime factors."
A lot of smart people were working very hard on this problem, and surely the overview article makes it sound a lot easier than it actually was!  But the article does make one feel one understands a little of the overview or "philosophy" of the proof.